In Try This 2 you graphed the simplest radical function possible: Did you notice the distinct shape that you graphed? You may remember this shape from Try This 1 in Discover. You have now seen two radical functions with this distinct shape. This shape is sometimes describes as one-half of a parabola opening to the right. The domain of the function is {x|x ≥ 0, y ∈ R} because you cannot take the square root of a negative number. The range of the function is {y|y ≥ 0, y ∈ R}.

Radical functions can be much more complex than the function you graphed in Try This 2. The general form of a radical function can be written as Do you see the similarities in this form to the general form for functions used in Module 1?

In Try This 3 you will investigate how the graph of radical functions changes in response to changes in the parameters a, h, and k of the general form of the function.

Try This 3

Open “Functions Involving Square Roots.”

Select the “Show domain” and “Show range” boxes in the gizmo.

This gizmo begins with a graph of Check that your graph, the domain, and the range from Try This 2 match this graph.

1. Use the slider to change the value of a, and record your answers in a chart like the following.
   
   

   a-value	Function	Domain	Range	Transformation of Graph and State the Stretch Factor	Sketch or Image
   1		{x|x ≥ 0, x ∈ R}	{y|y ≥ 0, y ∈ R}	none	Screenshot reprinted with permission of ExploreLearning.
   Positive value: ________
   Negative value: ________

2. Set the a-value back to 1. Use the slider and change the value of h, and record your answers in a chart like the following.
   
   

   h-value	Function	Domain	Range	Transformation of Graph and State the Value of the Translation	Sketch or Image
   0		{x|x ≥ 0, x ∈ R}	{y|y ≥ 0, y ∈ R}	none	Screenshot reprinted with permission of ExploreLearning.
   Positive value: ________
   Negative value: ________

3. Set the h-value back to zero. Use the slider, change the value of k, and record your answers in a chart like the following.
   
   

   k-value	Function	Domain	Range	Transformation of Graph and State the Value of the Translation	Sketch or Image
   0		{x|x ≥ 0, x ∈ R}	{y|y ≥ 0, y ∈ R}	none	Screenshot reprinted with permission of ExploreLearning.
   Positive value: ________
   Negative value: ________

Open Multiple Transformations. Click on “Quadratic” to deselect it, and click on “Square root” to select this type of function.

4. Change the a, b, h, and k sliders to explore what happens to the graph when these values are changed. In a chart like the following, summarize how the parameters a, b, h, and k transform the graph given in the general form
   
   

   Parameter	Value > 0	Value < 0
   a
   b
   h
   k

Save your responses in your course folder.